Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S

International audienceThe purpose of the book is to give a self-contained presentation of the techniques of time-frequency/time-scale analysis of 1-D signals and provide a set of useful tools to perform the analyses. Such a package should be especially attractive to the part of the scientific community interested in mathematical and practical issues, especially if they involve random or noisy signals with possibly nonstationary features. The use of the S language is a reflection of the intent to reach the statistical community that, despite the traditional interest in the spectral analysis of time series and the pervasive use of orthonormal wavelet bases, has seen very few attempts to understand the benefits of the continuous transforms. The first part of the book is intended to be a hands-on crash course on some of the major components of the time-frequency analysis of signals. A special emphasis is put on the analyses of noisy signals, and great care is taken to address the stationarity issue and describe the statistical significance of the spectral analyses and the denoizing procedures. The second part of the book is a reference manual for the library of S functions, which is written to perform all the computations relative to the examples described in the first part of the monograph